High School

It is known that in a box containing 12 bottles of wine, 2 are bad wines. Two bottles of wine are selected randomly from this box. If sampling is done with replacement, what is the probability that both bottles of wine are bad?

A) 0.177
B) 0.333
C) 0.027
D) 0.167

Answer :

When sampling is done with replacement, it means that after selecting a bottle, it is put back into the box before the second bottle is chosen. Hence, the correct option is (C) 0.027.

In this case, there are 12 bottles in total, 2 of which are bad wines.

The probability of selecting a bad wine on each draw is 2/12 = 1/6.

Since the sampling is done with replacement, the probability of selecting a bad wine on the first draw and then again on the second draw is:

P(both bottles are bad) = (1/6) * (1/6) = 1/36 ≈ 0.027

Therefore, the probability that both bottles of wine are bad is approximately 0.027.

Learn more about probability here:

brainly.com/question/31828911

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